7.4 Dispersion corrections as a controlled comparison

7.4.1 Ask a question that the correction can answer

Semilocal density functionals can miss long-range correlation important for molecular packing, layered solids and adsorption. An empirical dispersion correction adds a geometry-dependent contribution. It should not be treated as permission to abandon convergence, as a universal remedy for chemisorption, or as an independently fitted experimental adsorption energy.

This unexecuted ABACUS 3.9.0 case extends adsorption energies. Use an already checked neutral molecule-on-slab geometry and its clean slab and isolated molecule references. Start with a fixed-geometry comparison before allowing any coordinates to relax. Keep the same PBE pseudopotentials, matched LCAO numerical orbitals or PW basis, numerical resolution and reference stoichiometry. The selected molecule must have a physically plausible initial height; a wildly overlapping geometry is not a dispersion experiment.

The pinned manual documents none, d2, d3_0 and d3_bj choices. D3 automatic parameter selection for common explicit functionals is documented after 3.8.3. This recipe uses explicit PBE and checks the accepted damping settings. It does not generalize that automatic table to every custom Libxc expression or every development release.

7.4.2 Energy balance and two kinds of change

The comparison can be organized as

\[ E^{\mathrm{DFT+D}}(\mathbf R)=E^{\mathrm{DFT}}(\mathbf R)+E_{\mathrm{disp}}(\mathbf R),\qquad E_{\mathrm{ads}}=E_{AB}-E_A-E_B. \]

At a common geometry, the correction to adsorption is the difference between the three dispersion terms, not the combined-system term alone. At separately relaxed geometries, the change also includes a geometric response of the underlying DFT energy. Report which experiment you performed. A height scan can help separate the attractive long-range region from the repulsive short-range region, but its curve must be computed rather than inferred from the correction's name.

Damping changes how an asymptotic correction behaves at short distances. D3(0) and D3(BJ) are different models, not loose and tight settings of one numerical algorithm. Changing their coefficients is model modification. Increasing a periodic summation radius at fixed method is instead a numerical convergence test.

Open figure at full size

The plotted curves are explicitly schematic. Their minima and depths are not measured adsorption results, and no numerical binding energy is provided.

7.4.3 Worked paired INPUT deltas

Duplicate each of the three converged reference folders. Replace the functional and dispersion keys consistently; retain all other accepted INPUT settings, STRU and KPT appropriate to that reference.

# Branch A: fixed-geometry PBE baseline, ABACUS 3.9.0
suffix          ads_PBE_fixed
dft_functional  pbe
vdw_method      none

# Branch B: same geometry and numerical model, ABACUS 3.9.0
suffix          ads_PBE_D3BJ_fixed
dft_functional  pbe
vdw_method      d3_bj
vdw_cutoff_type radius
vdw_radius_unit Bohr
vdw_cutoff_radius 95

95 Bohr is a documented D3 starting summation radius, not the slab vacuum thickness and not an energy cutoff. Check the accepted PBE damping coefficients; do not add borrowed vdw_s6, vdw_s8, vdw_a1 or vdw_a2 values unless intentionally defining and documenting a different model. The dispersion coordination-number radius is a separate control (vdw_cn_thr and its unit selector); record it and test it when the target accuracy demands.

For each branch, also apply the same method to the clean slab and molecule. Their physical k meshes need not be identical to each other, but each reference must be independently converged and the method must match. A periodic isolated molecule can interact with its dispersion images even when its charge density barely overlaps them, so check box size again rather than assuming the old vacuum test suffices.

7.4.4 Workflow, outputs and relaxation

Compute the fixed-geometry triples first. Read the accepted correction, SCF termination and energy components from the complete OUT.<suffix>/running_scf.log. Preserve full output rather than relying on a parser that only retains the last generic total-energy token. If a separate dispersion contribution is printed, retain it for the energy balance, but never add it again to a total already containing the correction.

Increase the summation radius in a controlled series, while keeping all electronic settings unchanged. Check the adsorption energy as well as each total energy. An apparently large absolute change that cancels in the reaction energy can be acceptable; an apparently small total-energy change that does not cancel can matter. Independently test slab thickness, vacuum, lateral cell size and the molecule reference box.

Then, if the chosen release/basis supports the intended corrected forces and geometry path, relax the molecule and permitted slab layers with the same correction. Use a static high-accuracy final calculation. Compare the fixed-geometry and relaxed differences as separate rows; do not claim all of the final change came from a direct long-range term. Confirm the optimized structure represents the same adsorption site and chemical state before interpreting an energy difference.

7.4.5 Blank convergence and comparison table

Branch	Geometry definition	Radius (Bohr)
PBE	common fixed	not applicable
PBE-D3(BJ)	common fixed	95
PBE-D3(BJ)	common fixed	larger, recorded
PBE-D3(BJ)	relaxed, recorded	converged

Do not fill cells from illustrative plots. Choose an energy tolerance below the site-ordering or binding-energy resolution you intend to discuss. For LCAO adsorption, numerical-orbital completeness and basis superposition remain separate issues; a dispersion term does not remove them. For strongly polar or charged fragments, electrostatic finite-size effects also remain and need their own validated treatment.

7.4.6 Pitfalls, exercises and answers

Pitfalls. Adding D3 only to the adsorbed system creates an inconsistent reaction. Using a nonlocal van der Waals functional and then adding a separate correction without justification can double count correlation. Confusing the periodic summation radius with vacuum thickness leaves image interactions unchecked. Reusing different relaxed structures while calling the comparison vertical hides geometry effects. Taking a more negative adsorption energy as universally more accurate ignores the limitations of the chosen model.

Exercise 1. If the correction changes EAB by -a, EA by -b and EB by -c, what is its fixed-geometry effect on adsorption? Answer: \(\Delta E_{\mathrm{ads}}=-a+b+c\). The combined-system correction alone is insufficient.

Exercise 2. D3(BJ) and D3(0) disagree after both are numerically converged. Should you average them? Answer: not automatically. They define different damping models. Report the sensitivity, compare to an appropriate physical reference, and justify the model selection independently of numerical convergence.

7.4.7 Sources

Continue to performance benchmarking, keeping this distinction between physics and numerical controls.